Hilbert-space structure of a solid-state quantum computer: two-electron states of a double-quantum-dot artificial molecule

A quantum-dot hydrogen molecule was studied as the basic elementary gate for a quantum computer based on electron spins in quantum dots. By using both Hartree-Fock approximation and a molecular-orbital theory, the excitation spectrum of two electrons in two horizontally coupled quantum dots was determined. The dependence of this spectrum on an external magnetic field was also clarified.